LightBoard

"LightBoard" is a problem from the College Board's 2019 AP Computer Science A released exam. Let's take a look at it.

Get a copy of the problem from the College Board here. We're looking at problem #4 from that exam.

The LightBoard class models a two-dimensional display of lights, where each light is either on or off, as represented by a Boolean value. You will implement a constructor to initialize the display and a method to evaluate a light.

public class LightBoard { /** The lights on the board, where true represents on and false represents off. */ private boolean[][] lights; /** Constructs a LightBoard object having numRows rows and numCols columns. * Precondition: numRows > 0, numCols > 0 * Postcondition: each light has a 40% probability of being set to on. */ public LightBoard(int numRows, int numCols) { /* to be implemented in part (a) */ } /** Evaluates a light in row index row and column index col and returns a status * as described in part (b). * Precondition: row and col are valid indexes in lights. */ public boolean evaluateLight(int row, int col) { /* to be implemented in part (b) */ } // There may be additional instance variables, constructors, and methods not shown. }

(a) Write the constructor for the LightBoard class, which initializes lights so that each light is set to on with a 40% probability. The notation lights[r][c] represents the array element at row r and column c.

Complete the LightBoard constructor below.

/** Constructs a LightBoard object having numRows rows and numCols columns. * Precondition: numRows > 0, numCols > 0 * Postcondition: each light has a 40% probability of being set to on. */ public LightBoard(int numRows, int numCols)

(b) Write the method evaluateLight, which computes and returns the status of a light at a given row and column based on the following rules.

If the light is on, return false if the number of lights in its column that are on is even, including the current light.
If the light is off, return true if the number of lights in its column that are on is divisible by three.
Otherwise, return the light’s current status.

For example, suppose that LightBoard sim = new LightBoard(7, 5) creates a light board with the initial state shown below, where true represents a light that is on and false represents a light that is off. Lights that are off are shaded.

lights:

	0	1	2	3	4
0	true	true	false	true	true
1	true	false	false	true	false
2	true	false	false	true	true
3	true	false	false	false	true
4	true	false	false	false	true
5	true	true	false	true	true
6	false	false	false	false	false

Sample calls to evaluateLight are shown below.

Call to evaluateLight	Value Returned	Explanation
sim.evaluateLight(0, 3);	false	The light is on, and the number of lights that are on in its column is even
sim.evaluateLight(6, 0);	true	The light is off, and the number of lights that are on its column is divisible by 3.
sim.evaluateLight(4, 1);	false	Returns the light's current status.
sim.evaluateLight(5, 4);	true	Returns the light's current status.

Class information for this question

public class LightBoard private boolean[][] lights public LightBoard(int numRows, int numCols) public boolean evaluateLight(int row, int col)

Complete the evaluateLight method below.

/** Evaluates a light in row index row and column index col and returns a status * as described in part (b). * Precondition: row and col are valid indexes in lights. */ public boolean evaluateLight(int row, int col)